Average Error: 0.2 → 0.0
Time: 2.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r258969 = 1.0;
        double r258970 = 4.0;
        double r258971 = x;
        double r258972 = y;
        double r258973 = 0.75;
        double r258974 = r258972 * r258973;
        double r258975 = r258971 + r258974;
        double r258976 = z;
        double r258977 = r258975 - r258976;
        double r258978 = r258970 * r258977;
        double r258979 = r258978 / r258972;
        double r258980 = r258969 + r258979;
        return r258980;
}
↓
double f(double x, double y, double z) {
        double r258981 = 1.0;
        double r258982 = 0.75;
        double r258983 = 4.0;
        double r258984 = r258982 * r258983;
        double r258985 = r258981 + r258984;
        double r258986 = x;
        double r258987 = z;
        double r258988 = r258986 - r258987;
        double r258989 = y;
        double r258990 = r258988 / r258989;
        double r258991 = r258983 * r258990;
        double r258992 = r258985 + r258991;
        return r258992;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.75 + 4 \cdot \frac{x - z}{y}\right)}\]

  5. Applied associate-+r+0.0

    \[\leadsto \color{blue}{\left(1 + 4 \cdot 0.75\right) + 4 \cdot \frac{x - z}{y}}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{\left(1 + 0.75 \cdot 4\right)} + 4 \cdot \frac{x - z}{y}\]

  7. Final simplification0.0

    \[\leadsto \left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))